Mathematics, Form and Function: Difference between revisions

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Throughout his book, and especially in chapter I.11, Mac Lane informally discusses how mathematics is grounded in more ordinary concrete and abstract human activities. This section sets out a summary of his views on the human grounding of mathematics.

Mac Lane is noted for co-founding the field of [[category theory]], which enables a far-reaching, [[unifying theories in mathematics|unified treatment]] of mathematical structures and relationships between them at the cost of [[abstract nonsense|breaking away from their cognitive grounding]]. HisNonetheless, his views, &mdash;however informal, &mdash;are a valuable contribution to the [[philosophy of mathematics|philosophy]] and [[anthropology]] of mathematics<ref>On mathematics and anthropology, see White (1947) and Hersh (1997).</ref> which anticipates, in some respects, the much richer and more detailed account of the [[cognitive science of mathematics|cognitive basis of mathematics]] given by [[George Lakoff]] and [[Rafael E. Núñez]] in [[Where Mathematics Comes From]]. Lakoff and Núñez (2000) argue that mathematics emerges via [[conceptual metaphor]]s grounded in the [[embodied philosophy|human body]], its motion through [[space]] and [[time]], and in human sense perceptions.

The following table is adapted from one given on p. 35 of Mac Lane (1986). The rows are very roughly ordered from most to least fundamental. For a bullet list that can be compared and contrasted with this table, see section 3 of ''[[Where Mathematics Comes From]]''.